|MadSci Network: Earth Sciences|
Actually, there are a couple of theories I think you might be mixing together. One is continental drift, which describes how the continents move around on the surface of the earth. A second deals with the liquid state of the outer core and magnetic field reversals and the third describes how the physical pole of the earth "wanders" over time, sometimes pointing towards the North Star (Polaris) and sometimes not. I'll discuss each of these briefly.
Plate tectonics is a theory that describes how the continents rearrange themselves over time. According to this theory (which is very well-established and is accepted as fact) the continents ride on top of plates of crust. These plates move away from mid-ocean spreading centers (like the mid-Atlantic Ridge) across the face of the earth. At the other end, the oceanic crust dives down into deep-sea trenches to be recycled while the lighter continents collide and sometimes stick together. Right now, for example, North America is moving away from Europe towards Asia. In a few tens of millions of years we'll run into Japan (which is next to a trench, or subduction zone) and become part of Asia. It is thought that plate tectonics are driven by convection within the rock of the earth's mantle - although the rock is solid, over millions of years it can flow, just as ice in a glacier flows over time.
On to the second! Shortly after the earth formed, it was very hot. It's thought that most of the iron in the earth melted and, due to its high density, sunk to form the earth's core. This released a lot of gravitational potential energy, enough to melt the entire planet. Obviously the earth cooled down again and, over time, the core is cooling, too. As the iron in the liquid part of the core cools and crystalizes it becomes more dense than the surrounding liquid, so it sinks to the "bottom", forming a solid inner core completely surrounded by the molten iron outer core. Geophysicists think that the motion of the liquid iron flowing in the outer core helps to generate and maintain the earth's magnetic field and, periodically, turbulence and other as-yet-unknown fluctuations in the outer core cause the magnetic field to reverse polarity.
Finally, as the earth turns it behaves like a top spinning on the floor. Any spinning object will have an axis of rotation and, due to physics of spinning objects, this axis will "precess", or move slowly in space. If you look at a top you'll notice its axis will slowly turn as the top spins, although at a much slower rate. In the case of the earth, this means that the north pole (currently pointing at Polaris) is always moving and will someday point at another star. This complete cycle takes about 22,000 years. Putting all of these motions together gives some pretty interesting effects if you're trying to figure out where the north pole was at times in the past, but geologists have been able to reconstruct such records pretty convincingly for quite a long period of time.
For more information on all of these I'd recommend reading a good textbook such as Earth by Press and Siever. That will go into quite a bit of detail on all of these topics, and more. Another good book to read is Planet Earth by Cesare Emiliani.
Try the links in the MadSci Library for more information on Earth Sciences.